Single Comment

'It seems to me that Weissman's perfect strategy could be foiled by
allowing non-splitting moves'

This just makes it take longer, as the main exploit, as Rich Hutnik pointed
out, is that White is able to create 2 boards which advance its position,
and then use the one Black doesn't respond on for its next move.

If black has the option of just making one response and not splitting the
board, then a winning strategy for white is:

As before, White starts with e3 and e4. Black responds on one board, on the
other White plays Bishup c4 and Queen h5, both threatening f7.

Now, if Black does not respond on the board where White moved the Bishup,
then on this board White moves Queen h5, otherwise Black did not respond on
the board where White moved the Queen, and on that board white moves Bishup
c4. Either way, White has created a board with its Queen on h5 and Bishup
on c4, threatening Queen takes f7 mate, and White's other move is Knight
f3.

So Black responds on the board where White just moved the Queen or Bishup,
otherwise White mates with Queen takes f7. So, on the board where White
moved the Knight, white again moves Queen h5 or Bishup c4 threatening mate,
and splits the board with Knight g5, threatening Bishup or Queen takes f7
mate. Black is now threatened with mate on two boards and can only respond
on one. White mates on the other. Black has not even been able to make a
move on the board where the mate occurs.